Short-range scattering of Hartree type fractional NLS

Yonggeun Cho

doi:10.1016/j.jde.2016.09.025

Short-range scattering of Hartree type fractional NLS

Yonggeun Cho

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

8 Scopus citations

Abstract

In this paper we consider scattering problem for Hartree type fractional NLS with |∇|^α (1<α<2) and potential V∼|x|^−γ. We show small data scattering in a weighted space for the short range. The difficulty arises from the non-locality and non-smoothness of |∇|^α. To overcome it we utilize the method of commutator estimate based on Balakrishnan's formula.

Original language	English
Pages (from-to)	116-144
Number of pages	29
Journal	Journal of Differential Equations
Volume	262
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2016.09.025
State	Published - 2017.01.5

Keywords

Fractional NLS
Hartree type potential
Short-range interaction
Small data scattering

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1016/j.jde.2016.09.025

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title = "Short-range scattering of Hartree type fractional NLS",

abstract = "In this paper we consider scattering problem for Hartree type fractional NLS with |∇|α (1<α<2) and potential V∼|x|−γ. We show small data scattering in a weighted space for the short range. The difficulty arises from the non-locality and non-smoothness of |∇|α. To overcome it we utilize the method of commutator estimate based on Balakrishnan's formula.",

keywords = "Fractional NLS, Hartree type potential, Short-range interaction, Small data scattering",

author = "Yonggeun Cho",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2017",

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doi = "10.1016/j.jde.2016.09.025",

language = "English",

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AU - Cho, Yonggeun

PY - 2017/1/5

Y1 - 2017/1/5

N2 - In this paper we consider scattering problem for Hartree type fractional NLS with |∇|α (1<α<2) and potential V∼|x|−γ. We show small data scattering in a weighted space for the short range. The difficulty arises from the non-locality and non-smoothness of |∇|α. To overcome it we utilize the method of commutator estimate based on Balakrishnan's formula.

AB - In this paper we consider scattering problem for Hartree type fractional NLS with |∇|α (1<α<2) and potential V∼|x|−γ. We show small data scattering in a weighted space for the short range. The difficulty arises from the non-locality and non-smoothness of |∇|α. To overcome it we utilize the method of commutator estimate based on Balakrishnan's formula.

KW - Fractional NLS

KW - Hartree type potential

KW - Short-range interaction

KW - Small data scattering

UR - https://www.scopus.com/pages/publications/84995468823

U2 - 10.1016/j.jde.2016.09.025

DO - 10.1016/j.jde.2016.09.025

M3 - Journal article

AN - SCOPUS:84995468823

SN - 0022-0396

VL - 262

SP - 116

EP - 144

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Short-range scattering of Hartree type fractional NLS

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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